In this study, we consider the dynamics of a spinning tether system in an elliptical orbit in application to the Momentum Exchange Electrodynamic Reboost system. Momentum exchange tether systems have been studied in a variety of applications since Hans Moravec's early publication. It has recently been suggested that momentum exchange systems can be enhanced with electrodynamic reboost between payload transfers. The Momentum Exchange Electrodynamic Reboost system (MXER) has a projected tether span of up to 100 km, and spins rapidly with a period of 6-7 min. It is placed in an orbit with a low perigee of about 400 km and a high apogee of about 8000 km. To capture a payload at a perigee rendezvous, within a window of a few seconds, the motion of the system has to be predicted with very high precision, having acceptable position errors on the order of 1 m. While this level of precision is routinely achieved today for conventional (non-tethered) satellites, it is much more difficult to achieve for a 100 km long flexible tether system. It is the goal of this study to investigate theoretical aspects of the dynamics and offer a practical approach to high precision dynamic modeling of a typical momentum exchange tether system.